Apply median filter to an ECG without native MATLAB medfilt

I need to apply a median filter to an ECG(the ECG data is anexed bellow) to remove low frequency noise, so that a new filtered signal is generated.

However, I cannot use the native matlab function medilft (a new median filter function must me written without it) and it should allow the input of a variable s- the size of the neighbourhood used by the filter.

So, to obtain the filtered singnal, the is a final subtraction between the original signal and the filter:

signal_filtered(i) = signal(i) - signal_median(i)

Any help is greatly appreciated!

Cheers!

[Jan]

What have you tried so far? Do you have a specific question? The forum will not solve your homework.

[José Burgo]

Yes, when selecting sucessive lead elements to establish neighbourhoods of the ECG I have problems with the first or last elements, because the are no more elements to form the new neighbourhodd, for example:

with A=[ 1 2 3 4 5] with k(neighbourhood) = 3 ,

it´s ease to obtain median of [ 1 2 3] and [2 3 4] and [3 4 5],

but that would leave me with only 3 elements, and to perform the subtraction I need 5 elements ( same as the ECG)

Is there any way to correct this?

[DGM]

Edge conditions can be handled in various ways, but normally I just pad the array. In order to hang the window off the end of the vector, pad the ends of the vector by half the window width. You could do this by adding zeros, but replicating the end elements avoids adding a step discontinuity.

Answer 1

[Image Analyst]

If you don't have medfilt1 because you're missing the Signal Processing Toolbox, you can use a for loop and the median, which is part of base MATLAB.

signal = rand(1, 30);
signal_median = signal; % Initialize output signal
subplot(2, 1, 1);
plot(signal, 'b-', 'LineWidth', 2)
windowWidth = 3;
for k = ceil(windowWidth/2) : numel(signal) - floor(windowWidth/2) 
	signal_median(k) = median(signal(k - floor(windowWidth/2) : k + floor(windowWidth/2)));
end
hold on
plot(signal_median, 'r-', 'LineWidth', 2)
grid on;
title('Original and Median Filtered Signals')
legend('Original', 'Median Filtered')
% Subtract
signal_filtered = signal - signal_median;
subplot(2, 1, 2);
plot(signal_filtered, 'b-', 'LineWidth', 2)
yline(0, 'Color', 'k', 'LineWidth',2); % Draw black line along y=0 (x axis).
title('Difference Signal')
grid on;

[José Burgo]

Cheers! Adapting it to my introduced ECG and with an handmade median worked just great. Thanks a lot for your help :)

[Image Analyst]

A hand made median would require the use of sort(), unless you also did the sorting yourself. Not sure what functions you can't use, or why you can't use them, but glad you got it working. Thanks for accepting the answer. 🙂

What can be programmed "without any built-in functions" ? - MATLAB Answers - MATLAB Central

Answer 2

[DGM]

It's a simple sliding-window filter. Given a vector V:

1. define a window width W (an odd number is convenient)
2. pad V by padwidth = floor(W/2) elements on each end. (replicating the end values is convenient)
3. preallocate output vector to the same size as the original unpadded input vector
4. loop through the elements of V from padwidth+1:end-padwidth (the original part of the vector)
5. at each point k, sample a region around the current element V(k-padwidth:k+padwidth)
6. find the sample median (and difference if desired). The result should be a scalar.
7. the result at point k goes in the corresponding element of the output vector (i.e. k-padwidth)

[José Burgo]

Thanks! Helped a lot in correcting the ends!